↑

Properties

Label 370.2.c
Level $370$
Weight $2$
Character orbit 370.c
Rep. character $\chi_{370}(369,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $2$
Sturm bound $114$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(114\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(370, [\chi])\).

Total New Old
Modular forms 60 20 40
Cusp forms 52 20 32
Eisenstein series 8 0 8

Trace form

\( 20 q + 20 q^{4} - 16 q^{9} + 6 q^{10} + 20 q^{16} - 24 q^{21} + 10 q^{25} + 4 q^{26} + 20 q^{30} - 36 q^{34} - 16 q^{36} + 6 q^{40} - 8 q^{41} - 20 q^{46} - 16 q^{49} + 20 q^{64} + 4 q^{65} - 40 q^{71}+ \cdots - 164 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(370, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
370.2.c.a 370.c 185.d $10$ $2.954$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 370.2.c.a \(-10\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
370.2.c.b 370.c 185.d $10$ $2.954$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 370.2.c.a \(10\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(370, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(370, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)